next up previous contents
Next: Convective adjustment Up: Les paramétrisation physique du Previous: Radiation

Vertical turbulent mixing

The formulation of the vertical turbulent mixing is taken almost directly from the very simple scheme used in the LMD climate model. The effect of turbulent mixing on momentum and potential temperature is evaluated by the mean of a classical diffusion equation

equation603

where the turbulent mixing coefficient tex2html_wrap_inline5480 is computed as

equation613

in term of mixing length l and a diagnostic estimate of the turbulent energy

equation616

(the minimum value of the kinetic energy was set to tex2html_wrap_inline5484  m tex2html_wrap_inline5486  s tex2html_wrap_inline5488 ). In the case where tex2html_wrap_inline5490 , the vertical mixing coefficient can be expressed as a function of the Richardson number

equation629

as

equation633

For both momentum and potential temperature, the turbulent surface flux is computed as the product between the vertical gradient of the quantity (estimated between the surface value and that in the first atmospheric layer) and a drag coefficient tex2html_wrap_inline5492 given by:

equation638

where tex2html_wrap_inline5494 is the wind in the first atmospheric layer and tex2html_wrap_inline5496  m s tex2html_wrap_inline5488 . The diffusion equation is integrated with an implicit time scheme. In the simulations presented below, l was fixed to 35 m and tex2html_wrap_inline5502 to 2 tex2html_wrap_inline5504 , typical values used for terrestrial surfaces in the climate GCM.

we use the formulation developed by [8] for the terrestrial planetary boundary layer, in the form which has been implemented at ECMWF.

The drag coefficient is given by

equation647

where tex2html_wrap_inline5506 is the roughness length, z is the height of the middle of the first atmospheric layer, k=0.4 is the von Karman constant and

equation654

is the Richardson number where tex2html_wrap_inline5512 and ||V|| are the potential temperature and wind velocity in the first atmospheric layer, and tex2html_wrap_inline5516 the surface temperature. Two different functions f are used for momentum ( tex2html_wrap_inline5520 ) and potential temperature ( tex2html_wrap_inline5522 ). In either case, a different formulation is used depending on whether the atmosphere is stable ( tex2html_wrap_inline5524 )

equation659

equation663

or unstable ( tex2html_wrap_inline5526 )

equation667

equation672

As in the original terrestrial version, we use C=b=d=5.


next up previous contents
Next: Convective adjustment Up: Les paramétrisation physique du Previous: Radiation

HOURDIN Christophe
mardi, 9 novembre 1999, 17:34:37 MET